Incidentally, I am not sure where you got your etymology for your daughter's name, but Lauryn (Lauren) means "laurels," or "from Laurentum," a place in ancient Italy with lots of laurel trees. Olivia either means "olive tree" or, believe it or not, "elf-army," via the ancient Germanic name Alvar. So LaurynOlivia-- while very lovely-- does not meaning "new beginning."